Problems on Time and Work

Learn how to solve problems on time and
work in different situations when time required to complete a piece of work and
when the work done in a given period of time.

Case
I: If a person A completes a piece of work in n days, then work
done by A in one days = 1/n th part of the work.

Case
II: If a person A completes 1/n th part of
work in one day, then A will take n days to complete the work.

Now we will learn how to use the concept
of time and work for solving various problems.

Word problems on time and work:

1. Adam is thrice as good a workman as Brain and together they finish the piece of work in 15 days. In how many days will Adam alone finish the work?

Solution:

Adam’s 1 day’s work: Brain’s 1 day’s work
= 3 : 1

(Adam + Brain)’s 1 day’s work = 1/15

Now, divided 1/15 in the ratio 3 : 1

Therefore, Adam’s 1 day’s work = 1/15 × 3/4 = 1/20

Therefore, Adam alone can finish the work
in 20 days.

2.
Archie, Benjamin, Christopher can finish a piece of work in 10 days, 12 days
and 15 days respectively. If all the three work at it together, they are paid $
600 for the whole work. How should the money be divided among them?